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Standard XII

Mathematics

Condition for Two Lines to Be Perpendicular

A line inters...

Question

A line intersects $x -$ axis at $A (7, 0)$ and $y -$ axis at $B (0, - 5)$ . A variable line $P Q$ which is perpendicular to $A B$ cutting $x -$ axis at $P$ and $y -$ axis at $Q$ . If $A Q$ and $B P$ intersect at $R$ , find the locus of $R$ .

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Solution

$a = - 7, b = 5$
$x^{2} + y^{2} - 7 x + 5 y = 0$

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A line cuts the x - axis at A(7, 0) and the y - axis at B(0, -5). A variable line PQ is drawn perpendicular to AB. Cutting the x - axis at P and the y - axis at Q.
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A line intersects x−axis at A(7,0) and y−axis at B(0,−5). A variable line PQ which is perpendicular to AB cutting x−axis at P and y−axis at Q. If AQ and BP intersect at R, find the locus of R.

a=−7,b=5x2+y2−7x+5y=0

A line intersects $x -$ axis at $A (7, 0)$ and $y -$ axis at $B (0, - 5)$ . A variable line $P Q$ which is perpendicular to $A B$ cutting $x -$ axis at $P$ and $y -$ axis at $Q$ . If $A Q$ and $B P$ intersect at $R$ , find the locus of $R$ .

$a = - 7, b = 5$
$x^{2} + y^{2} - 7 x + 5 y = 0$